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add the governing equation.
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Phoenix Kyoma
Phoenix Kyoma
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Although there are similar questions, I am also struggling with the implementation of the following term in "my own code" by Finite Element Method, namely, $\nabla \phi \cdot \nabla \phi$. $\phi$ is a state variable such as scalar potential. I think the descritization of this term is much more difficult than that of advection term in N-S equation. If possible, please tell me how to descritize and implement the term by FEM. The equation to solve is as follows, $\frac{\partial \phi}{\partial t} = (\nabla\phi)^2 + \nabla^2 \phi.$

Although there are similar questions, I am also struggling with the implementation of the following term in "my own code" by Finite Element Method, namely, $\nabla \phi \cdot \nabla \phi$. $\phi$ is a state variable such as scalar potential. I think the descritization of this term is much more difficult than that of advection term in N-S equation. If possible, please tell me how to descritize and implement the term by FEM.

Although there are similar questions, I am also struggling with the implementation of the following term in "my own code" by Finite Element Method, namely, $\nabla \phi \cdot \nabla \phi$. $\phi$ is a state variable such as scalar potential. I think the descritization of this term is much more difficult than that of advection term in N-S equation. If possible, please tell me how to descritize and implement the term by FEM. The equation to solve is as follows, $\frac{\partial \phi}{\partial t} = (\nabla\phi)^2 + \nabla^2 \phi.$

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Phoenix Kyoma
Phoenix Kyoma
  • 85
  • 5

Implementation of nonlinear term in FEM

Although there are similar questions, I am also struggling with the implementation of the following term in "my own code" by Finite Element Method, namely, $\nabla \phi \cdot \nabla \phi$. $\phi$ is a state variable such as scalar potential. I think the descritization of this term is much more difficult than that of advection term in N-S equation. If possible, please tell me how to descritize and implement the term by FEM.